Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of ð ¶ ð ‘›

Arman Karapetyan

Abstract and Applied Analysis, 2010, vol. 2010, 1-23

Abstract:

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball ð µ ð ‘› and belonging to area-integrable weighted ð ¿ ð ‘ -classes with “anisotropic” weight function of the type ∠𠑛 ð ‘– = 1 ( 1 − | 𠑤 1 | 2 − | 𠑤 2 | 2 − ⋯ − | 𠑤 ð ‘– | 2 ) ð ›¼ ð ‘– , 𠑤 = ( 𠑤 1 , 𠑤 2 , … , 𠑤 ð ‘› ) ∈ ð µ ð ‘› . The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for ð ‘› = 2 ).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:354961

DOI: 10.1155/2010/354961

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